Mark Atkin with his father David. Photograph: Graham Turner for the Guardian

Mark Atkin first heard about the treasure when he was a little boy growing up in Northern Ireland. The family house was big and rambling with lots of secret passages – the perfect place to fire the imagination. Although his parents didn't often talk about their past, they did so enough for the story to become familiar; his paternal grandparents had left London to run a successful family rubber business in Lodz, Poland; his grandmother had later fled the Nazis with her two sons and gone back to London; his grandfather had stayed on till the last possible minute when he and the gatekeeper buried the family treasure before his grandfather made a miracle escape – he was one of the last four people out of Lodz, a story reported in detail on the front page of the News of the World in 1939.

Throughout his childhood, Mark thought about the treasure. But he didn't do anything about it. Childhood turned into adulthood and still he didn't act on it. Then, in 2000, his mother died and Mark and his father David decided to visit Latvia and Poland to explore their roots and distract themselves from their grief.

Latvia meant little to them. They travelled on to Lodz with low expectations. Astonishingly, they found things pretty much unchanged from 70 years ago, including the family home. They rang the bell and were told in no uncertain terms to get lost. Mark saw a couple of words in Polish printed on the building and wrote them down in case they gave any clues as to the new owners of their home. The two words were "military" and "research". The Polish army had taken over their house and turned it into a research base.

That was when Mark really started to develop an obsession about his father's childhood home – and the treasure. If the house had survived so long perhaps the treasure had too. He began to think of it as the family treasure – not simply their property, but also their history. And he wanted it back. Mark knew his grandfather had spent much of the war interned in civilian camps (he had left London and gone to Denmark, where he was captured by the Gestapo and sent to Poland) but he had died before he was born. If Mark could reclaim the treasure, perhaps he could somehow reclaim his relationship with his grandfather. Perhaps it would bring him closer to his father and unite the many disparate elements of his family.

Mark had always felt unsure of his identity. He looked Jewish but he wasn't because his father had married a gentile, and in Judaism it is the mother's bloodline that is followed. Actually, it was more complicated than that; his father also looked Jewish but he wasn't – his father had also married a gentile. Yet Judaism had shaped so much of their lives. After all, they had run away from Poland in the first place because they were regarded as Jewish. Throughout his childhood he had been on the move – from Northern Ireland to Leicestershire to London, and some more. Where did he belong? He didn't have a clue. The more he thought about the treasure, the more symbolic weight it assumed.

"I'd talk to my brother Nigel about it. We'd sit in a pub every so often and think about it. We wanted it kept – whether in the bosom of the family or in the town didn't matter, as long as it didn't get crushed under a steamroller or sold on the black market."

So Mark told his father he would like to return to Lodz and dig up the treasure. David looked at him as if he was bonkers. "I know it would be opening up a can of worms," Mark told David. "Big worms," David replied. David felt the treasure belonged to a horrific past that he had no wish to revisit.

But Mark convinced him otherwise. Not only that, he persuaded him to turn their real-life adventure into a film to be shown on television next week. The documentary is the closest you'll ever get to a Holocaust romp – part Simon Wiesenthal, part Enid Blyton, played out by a cast of Woody Allenesque eccentrics, it's an affecting and often funny look at family life through three generations.

In Poland in the 1930s, Mark's grandparents were sharing the house with their relatives, the Schrages, who ran the rubber company with them. The Schrages also escaped the Nazis, moving first to Cuba and then to Los Angeles where they thrived in the automobile industry. Mark decided the first step was to visit them in LA to get their blessing to hunt the treasure and see if they had any tips. Ah, the treasure, they said. Of course they knew about the treasure – a bath tub of gold and silver was said to have been buried in the garden. Oh, and there were also two Rembrandts hidden along with it, they added.

Then Mark went to Lodz, embarking on what turned out to be a bureaucratic nightmare. The military wouldn't let him search the house or garden. He went to the mayor of Lodz for help and eventually he was told he could dig up a small area in the back garden. A few days later, David, along with Mark's two brothers, joined him outside the old family home to hunt down the treasure. Mark became more and more frustrated the more obstacles he faced. He visited a clairvoyant and a rabbi for advice. Both told him the treasure was probably still there, but the most important treasure in his life might be closer to home – in his family.

And this is really what the film is about. Family. Mark seems to have made it partly as a way of documenting David's life – when they started filming two years ago, his father had already been diagnosed with early-stage dementia. His memories of the distant past were vivid and detailed, but the here and now was slipping from his grasp. David, who spent his working life developing tennis and golf balls and working on Daleks for Dr Who, has a lovely way with words when he can find them. "My father was always getting into trouble," he says. "Disaster followed him – if he walked into a room, the ceiling would cave in."

David says that because his dad spent so many years away in war camps, he was an absent father. And when they did get together, David's abiding memory is of them standing together, uncomfortable, not knowing what to say.

Meanwhile, Mark has a different take on the grandfather he never met. He regards him as a romantic adventurer who might just help him to make sense of his own life. Just as David felt the absence of his father as a boy, Mark felt the absence of David when he was growing up. "A lot of time when I was young, my dad was away working and we were always struggling to catch up with him. I became a lot closer to him when my mum died."

We're on a train to Battle in Sussex, where the Battle of Hastings took place and where David, now 82, lives by himself in a small house. Mark, 47, a trainer in digital media, is talking about why it was so important for him to track down the treasure. "Some property developer will buy that building, and if it's there they'll come across it and it will disappear. What a tragedy that would be when there is a chance to do something about it. If the Nazis didn't manage to get it and the communists didn't manage to get it but the capitalists did, that would be a gross injustice. And I was the only person who could possibly stand in the way of that happening." He says in every family there tends to be a self-appointed keeper of the stories, and that is his role in the Atkin family.

Was the value of the treasure important? "No, it was the sense of injustice." He says a visit to the Jewish Museum in Berlin made him all the more determined to track it down. "There was a battered old suitcase with a comb and collar and spoon in it, and these were the things that some guys had taken with them from Germany to Argentina. And some family had just kept that suitcase ... I found that quite profound."

It was a way of reclaiming his history? "Absolutely, and reuniting me with the grandfather I never met, who somehow I feel I have quite a connection with. Physically we looked quite similar and he was called Jack, and my friends all called me Jack through my childhood because my nose was even more prominent in those days – Jack for jackdaw. I liked that because it was my grandfather's name."

How would it change his life if he found the Rembrandts? He looks at me, astonished by the question. "I've never thought of it in those terms."

Mark says he's never been interested in the financial aspect of his quest.

We reach David's modest house in Battle. Although there were times when he made a good living, he could never emulate the lifestyle he was accustomed to as a little boy. David seems surprised to see us – he has forgotten that we're coming. Mark and David have a great relationship – David calls him Little Herbert (partly because he can't always remember his name and partly because he always had done) and they make each other laugh easily.

Mark brings out old family photographs and bits and pieces from the camps, and this is when you realise just how different the lives of Jack, David and Mark have been. Here is a bunch of metal keys with Stalag 13A printed on them; a wooden cow Jack carved in the camps; pictures of men in drag from the dramatic productions they put on in the camps.

However much trouble David might have keeping up with the present, he knows every story behind the photographs. He talks about the day he, his mother and younger brother left Poland and their three-day train journey to safety. "She was a hopeless traveller. She just passed out on the train and I had all the documents. I was 10 or 11 years old, in charge of our travel, with my little brother who, thank the Lord, was a blond boy. At one point, to my horror, a fellow in jackboots came in for the documents, and he had SS on his lapel. My brother, who had been looking out of the window with his telescope, turned round, stuck the telescope up the SS man's bum and said, 'Stick 'em up!' I don't think that happened to him often. He said, 'I surrender!' when he saw this little blond boy."

When they reached Berlin, they stopped to eat in a swanky restaurant. The way David tells the story, it could have happened yesterday. "It was like a hunting lodge and we were well looked after and the maître d' said, 'What great misfortune, you poor things. If only you'd been here 20 minutes earlier – the Führer himself was here.' Dad later said thank God he wasn't there because everyone else would have gone 'Sieg Heil' – and there is no way I would have done that. And if we hadn't we would have been in deep trouble." He pauses. "Yes, I've had a fairly interesting childhood," and he giggles like a little boy.

As a young boy, Mark knew little about his Jewish roots. Then, as he got older, he was invited to bar mitzvahs and weddings, and discovered more about the family's past. "My Great-Uncle Hermann, from Latvia, would always make the speeches and he'd refer to the people who weren't there." Eventually, Mark realised that Great- Uncle Hermann meant those family members who had been killed in the Holocaust. "The impact of that on me was immense."

Mark has never been so aware of his Jewishness as when he was in Lodz. Between the wars, Lodz was 36% Jewish, but few Jews remain today. "Whenever the military were looking at me I felt they were thinking, I know who you are and I know what you're doing here." At one point soldiers emerged with their guns angled in a less than friendly manner. Was he afraid? "No, I just felt overtaken by a feeling of high indignation, that sense of injustice. I stood my ground. I didn't care if they wanted to lock me up – fine, I'd make a diplomatic incident of it."

Meanwhile, David sat in the Lodz garden in his cowboy hat, taking in the sun and waiting till they had finished and it was time for a couple of glasses of wine. After they built a secret tunnel in an attempt to find the treasure, the Polish army found out what had been going on and things came to a head. Mark was told he would be in serious trouble unless he stopped digging. He was extremely put out, but David seemed relieved. Returning to his old house, he says now, had been traumatic. "Going through the big double gates I'd left as a boy, and I've never seen anything like them again, when I went back it all came in on me. I knew it all so well. It was all a bit much, it all crowded in on me. It was all there, my childhood was suddenly there."

Did that upset him? "Somewhat."

Now they are back in his garden in Battle, he is much happier. "The worst thing that could have happened is that we found the treasure," David says. "It would only be a hassle."

"What would the problems be if I found it, Dad?" Mark says.

David looks at his son and smiles. "Well, I can't imagine the Polish authorities just saying, 'Oh, is that your treasure you're taking out? Carry on!' No way, Little Herbert. It would all be hassle."

Mark knows all about the hassle, but still believes his mission was – and is – worthwhile. Now there is talk of the Atkins and the American side of the family buying the house in Lodz back from the Polish authorities. "The worst thing is, so many people would want a share of the treasure," David says.

"I think you're right, but I'll think about that when it happens," Mark replies.

They are sitting in the garden in Battle having a cuddle and giggle. "How did we get ourselves into this situation?" David asks his son repeatedly. No, he says, he wasn't interested in the treasure before the trip to Poland and he certainly isn't now. "It's never been a priority in my life to find it and get it. Thank you, but no."

True Stories: Digging for Grandad's Gold is on More4 on Tuesday 10 August